In fluid dynamics, the volumetric flow rate is defined as the volume of a fluid flowing through a point per unit time. The volumetric flow rate is in direct proportion to the average flow velocity of the fluid and the cross-sectional area of the passage through which the fluid is flowing.Q=Aν  (Equation 1)                Where        Q Volumetric flow Rate        A Cross-sectional Area        ν average flow velocity        
The difference between the volumetric flow rates of two fluids is known as the differential volumetric flow rate. For example, for two fluids flowing at a volumetric flow rate of Q1 and Q2, respectively, the differential volumetric flow rate (ΔQ) is:ΔQ=|Q2−Q1|  (Equation 2)
The differential volumetric flow rate between two fluids can be used to generate a thin stream of one of the fluids surrounded by the other fluid. The thin stream generated by using the differential volumetric flow rate between the two fluids can be utilized for various purposes. For example, in a flow cytometer, a thin stream of a sample fluid such as blood can be analyzed for its cell count, chemical composition, and the types of cells or suspended particles in it. Other examples of the sample fluid include, but are not limited to, urine, saliva and other body fluids. To generate the thin stream of the sample fluid, a stream of the fluid, annularly enveloped by a sheath fluid, is made to flow through a converged section of a cuvette or a funnel. Examples of the sheath fluid include, but are not limited to, saline and water. After passing through the converged section, the diameter of the converged stream of the sample fluid is further reduced by the effect of the hydrodynamic forces generated due to the differential volumetric flow rate between the sample fluid and the sheath fluid. This technique of generating a thin stream of the sample fluid by using a differential volumetric flow rate between the sample fluid and the sheath fluid is known as hydrodynamic focusing. The intensity of hydrodynamic focusing depends on various factors such as the type of sheath fluid and sample fluid used, the required stream diameter of the sample fluid, the geometry of the converging section, the differential volumetric flow rate, and the like. Therefore, to obtain a particular stream diameter of the sample fluid by using a specific sheath fluid, a specific differential volumetric flow rate needs to be maintained between the sample fluid and the sheath fluid.
There are various methods for obtaining the differential volumetric flow rate. In one of the existing methods, the differential volumetric flow rate is maintained by controlling the respective pressures of the sample fluid and the sheath fluid flowing through a flow circuit. The existing method is based on the relationship between the volumetric flow rate of a fluid and the fluid pressure, as detailed by Equation 3 below.QαΔP, when the flow resistance (R) of the flow circuit is constant  (Equation 3)                Where        Q Volumetric flow rate        ΔP Pressure differential between the inlet and the outlet of the flow circuit        
In this method, the sheath fluid and the sample fluid are pressurized at different pressures by their respective pressure sources. Thus, the volumetric flow rates of the sample fluid and the sheath fluid are controlled by independently controlling their respective pressures. Consequently, the differential volumetric flow rate between the sample and the sheath fluid can also be controlled.
Since the sample fluid and the sheath fluid are pressurized by two different sources, the pressure from both the pressure sources, and the pressure variations thereof, need to be synchronized to maintain a constant value of the differential volumetric flow rate. The differential volumetric flow rate is maintained at a constant value to generate a steady value of the hydrodynamic forces, which in turn maintains a constant diameter of a core stream of the sample fluid in the center. The constant diameter of the core stream is required for analysis in various systems, for example, a flow cytometer. For the purpose of maintaining a constant differential volumetric flow rate, a feedback system with two separate regulators can be provided. This feedback system can sense a change in the pressure of one of the fluids, for example, the sample fluid and correct it or synchronously regulate the pressure of the other fluid, for example, the sheath fluid. The feedback system can include mechanical links, electronic regulators, sensors, and combinations thereof. However, the use of the feedback system makes the system and method complex, error-prone and expensive. Very often, the feedback system tends to function erratically due to changes in temperature, atmospheric pressure and various other factors. Further, the feedback system can become inaccurate due to wear and tear of the mechanical parts and a drift in the electronic parts. Typically, the mechanical parts or electronic regulators operate within a tolerance zone, for example, a pressure regulator may have a positive and negative tolerance value of 0.02 pounds per square inch (psi). It is possible that at some point of time, a first pressure regulator can operate at a positive extreme of the tolerance zone and a second pressure regulator can operate at a negative extreme of the tolerance zone. For example, for maintaining a differential pressure of 0.5 psi, where the first fluid is at 5 psi and the second fluid is at 4.5 psi the first pressure regulator maintains a pressure of 5.02 psi and the second pressure regulator a value of 4.48 psi. Consequently, a differential pressure of 0.54 psi (5.02−4.48) is obtained resulting in a cumulative error in the pressure differential of 0.04 psi, (0.54−0.50) affecting the differential volumetric flow rate between the sample fluid and the sheath fluid. Thus, it becomes difficult to synchronize the pressure variation(s) between the two pressure sources, especially within the tolerance zones. As a result, it becomes difficult to maintain a focused sample fluid stream in devices such as a flow cytometer. Furthermore, the regulators used in the feedback system are expensive. Moreover, the use of two pressure sources increases the cost of the system.
In light of the foregoing, there is a need for providing a simple and cost-effective system and method for obtaining the differential volumetric flow rate and hydrodynamic focusing.